System for superresolution based estimation of control signals in a communication system

ABSTRACT

A system for wireless communication between a base station  30  and one or more remote stations  32  and  34  wherein a desired signal has associated therewith an identifier tone (a SAT in the vernacular of the AMPS system) and wherein interfering signals may have associated therewith identifier tones at different frequencies. A superresolution technique is used in the system to process the received data and to determine the relative magnitudes of any identifier tones which may be present in the received data. In the disclosed embodiment, the superresolution technique utilized is a least square error process. The resulting estimates are used by the system to facilitate the communication function.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to that disclosed and claimed inco-pending U.S. patent application, Attorney Docket Number TI-25707,filed on the same date as this application. This invention relates tothe use of superresolution techniques for the purpose of identifying areceived signal from a class of signals which could possibly be receivedand, in the preferred embodiment, to the use of such techniques in anAdvanced Mobile Phone System

[0003] 2. Background of the Invention

[0004] The AMPS is the most common cellular telephone standard in theUnited States. Each phone conversation uses two 30 kHZ bandwidthfrequencies, one for the uplink (mobile phone to the base station) andone for the downlink (base station to the mobile phone). Since there area limited number of frequencies available, it is common to reusefrequencies throughout the network. In other words, several basestations which are assigned the same frequencies are separated by somedistance to keep the interference at tolerable levels.

[0005] In spite of the spatial separation, it is still possible for amobile telephone or base station to detect the wrong signal(conversation). To help minimize this possibility, the AMPS systemincorporates Supervisory Audio Tones (“SATs”) in each transmission.There are three distinct SATs. These are at frequencies of 5970 Hz, 6000Hz, and 6030 Hz. Each base station is assigned one of the SATs, andtransmits this tone along with the audio conversation. The mobiletelephone detects the received signal, filters the SAT from the audio,notes which tone was received, and transmits the same tone back to thebase station on the uplink frequency. Similarly, the base stationdetects the received signal, filters the tone from the detected audio,and notes which tone was received. Should either the mobile telephone orthe base station determine that an incorrect SAT was received(indicating a transmission from an interfering user), the audio is gatedoff so that the users do not hear the incorrect conversation. Shouldthis situation (detection of the incorrect SAT) persist, correctiveaction such as reassignment of the phone call to a different channel orultimately dropping the call can be performed.

[0006]FIG. 1 illustrates a prior art apparatus which can be used todetermine which of the possible SAT tones has been received with a givenFM signal. The FM input signal 2 is demodulated in demodulator 4 and isthen coupled to the inputs of three parallel bandpass filters 6, 8, and10, each centered at one of the SAT frequencies, and each having abandwidth of 30 Hz. The delay time of the signal through the filter isroughly the inverse of the bandwidth, that is about 33 msec in thepresent case. Because of the presence of surrounding cells, the receivedFM input signal may contain energy at any or all of the SAT frequencies.The filter outputs represent the amount of such energy at each of thethree frequencies. The amplitudes of SAT signals at each of the SATfrequencies are then estimated by a short averaging process in amplitudeestimators 12, 16, and 18. SAT amplitude comparison logic circuit 20then determines whether or not the signal having the largest SAT signalis at the correct frequency. While the 33 msec filter delay time isacceptable in some applications, that time is unacceptably long inothers. Such is the case where the SAT identification is to be used inconnection with adaptively forming the beam pattern of the antenna usedat the base station of the system.

SUMMARY OF THE INVENTION

[0007] There is disclosed a communication system for receiving an inputwhich includes a desired signal as well as interfering signals, at leastsome of said desired signal and interfering signals having associatedtherewith one of a plurality of identifier components, the identifiercomponent associated with said desired signal being different than theidentifier components associated with at least some of said interferingsignals. The system comprises an identifier subsystem for using asuperresolution process to estimate the relative magnitudes of theidentifier components associated with the desired signal and interferingsignals which may be present; a receiver subsystem for receiving saidinput and for converting the input to a form usable by said identifiersubsystem; and apparatus responsive to the relative magnitude estimatesproduced by said identifier subsystem and operable to facilitate thecommunication function of said system. In the preferred embodiment, thesuperresolution process used is a Least Square Error (“LSE”) estimationprocess. Examples of other superresolution processes include MultipleSignal Identification and Classification (MUSIC), Estimation of SignalProperties by Rotational Invariance Techniques (ESPRIT), and MaximumLikelihood.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008]FIG. 1 is a block diagram of a prior art structure for determiningthe relative amplitudes of SATs which may be present in the receiveddata.

[0009]FIG. 2 is a graphical illustration of an AMPS system.

[0010]FIG. 3 is a surface spatial representation of an area 40 of thesurface of the earth to be served by an AMPS system.

[0011]FIG. 4 is a block diagram showing the structural elements of theinvention.

[0012]FIG. 5 is a detailed block diagram of the receiver portion of theadaptive antenna.

[0013]FIG. 6 is a symbolic representation of the adaptive antenna andLSE processing within the digital signal processor.

[0014]FIG. 7 is a flow chart summarizing the operation of the adaptivebeam forming process performed in the digital signal processor.

[0015]FIG. 8 is a flow chart illustrating the steps involved inobtaining the estimates of the relative sizes of the SAT tones presentin the received data.

[0016]FIG. 9 shows representative values of SAT estimates resultingfrom. a computer simulation of the LSE process.

[0017]FIG. 10 illustrates the variability of the estimates resultingfrom the computer simulation as a function of the number of samplesused.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0018]FIG. 2 is a graphic illustration of the components of a wirelesscommunication system such as AMPS. A base station 30 serves as the focalpoint of the system. Users such as in an automobile 32 or on foot 34,seeking to communicate with each other, do so under the control of thebase station 30. While the antenna pattern of the base station is shownas roughly omnidirectional, in accordance with the principles of thisinvention, the pattern can be caused to be highly directional.

[0019]FIG. 3 is a surface spatial representation of an area 40 of thesurface of the earth to be served by an AMPS system. The area is dividedinto a plurality of hexagonal shaped regions, each to be served by asingle base station. One such region 42 is labelled A₁. Within such aregion, the base station has available for its use about-sixtyfrequency-pair channels, each frequency having a 30 kHz bandwidth. Aspreviously noted, the base station uses a pair of frequencies incommunicating with any particular user or mobile station, one frequencyfor the uplink and one for the downlink. The frequency-pair forms onetwo-way communications channel. Given the relatively large number ofchannels available to this base station, it is able to use differentpairs of frequencies to communicate with each mobile station in itsregion and thereby avoid cross communication between mobile stations.

[0020] Audio information is transmitted by using the audio signal tofrequency modulate the carrier frequency. Typically this audioinformation is band limited to about three kHz. In addition to carryingthe audio information, the carrier frequency is further frequencymodulated by one of the SAT signals which reside at or very near sixkHz. In FIG. 3, the subscript 1 in the A₁ designator is used to indicatethat the lowest of these three SAT frequencies, 5970 Hz will be used forall transmissions in region 42.

[0021] Surrounding and immediately adjacent to region 42 are six otherregions such as regions 44 and 46. Each of these six regions will beassigned a complement of carrier frequencies different than thoseassigned to region 42. Further, the assignment of carrier frequencies ismade in such a way as to ensure that no two adjacent regions will havethe same complement. Regions 44 and 46 are labelled A₂ and A₃ toindicate that the SAT signals used to frequency modulate the carrierfrequencies in these two regions will be at 6000 Hz and 6030 Hzrespectively. These second two SAT signals are used in each of the otherfour regions surrounding region 42, and are used in such a way that notwo adjacent regions will have the same SAT frequency.

[0022] Surrounding this first ring of regions is a second ring ofregions such as region 48. Again, the sets of channel or carrierfrequencies are assigned to these regions in such a way as to ensurethat no two adjacent regions will have the same complement of carrierfrequencies. This is true despite the fact that some of the complementsof carrier frequencies used in region 42 or in the first ring ofsurrounding regions must be used again in the second ring.

[0023] Also in the second ring, the subscripts 1, 2 and 3 are used todenote which of the three SAT frequencies are used in the variousregions of this ring. In region 48, for example, the lowest SATfrequency, 5970 Hz is used just as it is in region 42. Given the factthat only three SAT frequencies are available, it is inevitable that,while it can normally be provided that no two adjacent regions will usethe same SAT frequency, such duplication must occur in relativelyclosely spaced regions such as regions 42 and 48. Where such duplicationoccurs, however, efforts are made to ensure that and two closely spacedregions which use the same SAT frequency will not also have the samecomplement of carrier frequencies.

[0024] Now, let it be assumed for purposes of illustration that the samecomplement of carrier frequencies is used in both regions 42 and 49. Itmay happen then that the base station of region 42 may receive afrequency modulated signal from a mobile station which is locatedoutside its own region, such as in region 49. The base station in region42 must be able to recognize this as an anomalous signal and notrespond. To do so it must demodulate the frequency modulated signal andidentify the frequency of the SAT signal associated therewith. In thiscase it will determine that the SAT frequency of the received signal is6030 Hz rather than the 5970 Hz used in region 42. The base station inregion 42 will, therefore, reject this as an anomalous signal.

[0025] A block diagram of the system is shown in FIG. 4. The adaptiveantenna is comprised of a series of antenna elements 50-52. In a typicalapplication, these elements have identical individual beam patterns andrange in number from two to eight, although other numbers of elementsare possible. The outputs of these antenna elements are coupledrespectively to a series of receivers 54-56. The receivers serve todownconvert the desired frequency spectrum to baseband (zerointermediate frequency) or some other low intermediate frequency. Thedownconverted signals are then converted to quadrature signals andcoupled respectively to a series of A to D converters 58-60. The outputsof each of the A to D converters are digitized I (in phase) and Q(quadrature) signals. The digitized I and Q signals from each of theconverters provide the inputs to the digital signal processor (“DSP”) 62which performs the adaptive antenna processing and also employs the LSEprocessing to generate an estimate of the amplitude of all of the threeSATs which may be present. DSP 62 may be any of various models in theTMS320 series such as the model TMS320C52 available from TexasInstruments Incorporated of Dallas, Texas. It has been demonstrated thatresolution times of approximately 0.005 seconds are achievable using theLSE process. While the adaptive antenna output signal is coupled throughbase station interface hardware 64 to base station 66 at all times, oncethe antenna has been adapted to focus the beam pattern on the correctincoming signal, this signal will be the primary component in theantenna output. In addition, the SAT identification information, whichhas been accomplished by DSP 62, can optionally be passed on to basestation 66.

[0026] The structure of one of receivers 54-56 is shown in greaterdetail in FIG. 5, it being understood that each of the other eightreceivers in this embodiment will have identical structures. The outputof antenna 50 is coupled to a front end filter 51 which serves to limitthe spectrum of the signal which is passed to low noise amplifier(“LNA”) 53 and thereby prevent saturation of the LNA by spurioussignals. The output of LNA 53 is coupled through image reject filter 55to the input of mixer 57 which has a 795 mHz local oscillator input andserves to downconvert the 840 mHz signal to a 45 mHz intermediatefrequency. The mixer would also mix a 750 mHz image to the sameintermediate frequency, but this is prevented by the image rejectionfilter which removes the 750 mHz components from the input of mixer 57.

[0027] The output of this first mixer 57 feeds a 30 kHz bandpass filter59 and a NE627 IF amplifier/downconverter 61 available from PhilipsSemiconductor located in Sunnyvale, Calif. Filter 59 is the final filterin the signal path and sets the A/D conversion bandwidth at the AMPSspectral bandwidth of 30 kHz. The NE627 provides IF amplification and,with a second local oscillator input of 44.9 mHz, mixes the signal downto the second IF of 100 kHz. The 100 kHz intermediate frequency isfurther amplified by amplifier 63 and then mixed to baseband by anRF2702 quadrature downconverter 65, available from RF Micro Devices,Inc. located in Greensboro, N.C. The RF2702 divides a third localoscillator signal at 800 kHz down to 100 kHz, and uses the divided downsignal to mix the 100 kHz signal to inphase, I, and quadrature, Q,output baseband signals. These signals, after further amplification byamplifiers 37 and 69, provide the inputs to A to D converter 58 of FIG.4.

[0028] The adaptive antenna and LSE processing within DSP 62 areillustrated symbolically in FIG. 5. The signals from antenna elements50-52 are first applied to complex weight multipliers 70-72. While, inthe interest of clarity, the filtering and digitizing elements are notshown in FIG. 6, the actual inputs to the multipliers are the digitizedI and Q signals. In FIG. 6, the N complex numbers comprising one samplein time from each of the elements are designated as the x,. For anygiven sample time, j, these N complex numbers can be thought of ascomprising a row vector, X_(j), having the elements, x_(i), i=1, 2, . .. , N. In each multiplier, the complex input signal, x_(i), ismultiplied by a complex weighting factor, w_(i)*. The N complex weightscan also be thought of as comprising a column vector, w*, having theelements, w_(i)*, i=1, 2, . . . , N. The computation of values for thew_(i) and w_(i)* (where the asterisk (*) denotes the complex conjugate)will be discussed below. The weighted input signals are then summed asshown at summer 74 to form a digitized complex antenna output signal 76which will hereinafter be generally designated as y. The variable yactually represents a time sequence of sampled values, y_(j), j denotingthe time of the sampled value in y. At any instant, j, the value of y,is the inner or scalar product of the vectors x_(j) and w*. Expressed invector notation, this is:

y _(j) =x _(j) ·w*  (1)

[0029] In Equation 1, the vector, w*, is a vector in which each elementis the complex conjugate of the corresponding element in the vector, w.

[0030] Each sample, y_(j), is then used to generate the value of thesample itself, normalized to a constant modulus of one. This normalizedversion of y_(j) will be designated as d_(j) and is equal to the ratio,y_(j)/|y_(j)|, where |y_(j)| represents the absolute value of y_(j).While the amplitude of y will, as the result of variables in the physicsof electromagnetic wave propagation, vary from time to time, thenormalized y will have a constant amplitude or constant modulus. Thedifference between y_(j) and the normalized y_(j) is shown symbolicallyat 78 as an error signal ε_(j). While, in the preferred embodiment, theerror signal, ε_(j), is not actually determined, its definition, asillustrated in FIG. 6, is necessary to an understanding of the followingdevelopment. Each of the y_(j), d_(j) and ε_(j) where j=1, 2, . . . canbe used to form respective column vectors y, d and ε.

[0031] The antenna output signal, y, is also demodulated at 80 and usedas the input to the SAT amplitude estimation processor 82. The SATidentification provided by this processor is used in the adaptiveantenna process as will hereinafter be described. In one embodiment ofthe invention, the adaptive antenna and SAT estimation processors willform integral parts of a base station. Alternatively, in this disclosedembodiment, where it is desired to add the adaptive antenna capabilityto an already existing base station, apparatus as described to thispoint can comprise a stand-alone beam forming system, tine output ofwhich is an input signal to the associated base station. In this case,the signal y, after appropriate formation of tee desired antenna beampattern, is reconverted up to the R: frequency signal which is expectedby the base station hardware. This is shown diagrammatically in FIG. 6where the signal y is also shown as an optional input to the basestation and is accomplished by the base station interface hardware 64 ofFIG. 4. Base station interface hardware 64 accomplishes the mirror imagefunction of the apparatus illustrated in FIG. 5 and, as is wellunderstood by those skilled in the art, can be accomplished with relatedhardware. In such an embodiment, the SAT identification process, whichhas already been performed once for purposes of adapting the antenna,may be repeated at the base station for the purpose of identifying theproper signal reception. Alternatively, the identity of the SAT,determined at block 82 of FIG. 6, can be transmitted to the base stationfor its use.

[0032] Still with reference to FIG. 6, the SAT identification providedby SAT extraction processor 82 provides an input to a beam forming orfocusing subsystem 71. Focusing subsystem 71 includes most of theelements portrayed in FIG. 6 as well as apparatus to perform additionalfunctions yet to be described. In addition to the SAT identification,the beam forming or focusing function utilizes the vector, d, that isthe vector of samples y, each normalized to a constant modulus of one,as well as the current set of weights, w₁-w_(n), and a series of thedata samples, x₁-x_(n). As hereinafter described in greater detail, inthe event that the SAT identification provided by SAT extractionprocessor 82 indicates that the signal on which the beam is currentlyfocused does not contain the desired SAT, a nulling subsystem 72, whichis part of focusing subsystem 71, functions to re-initialize the set ofweights, w₁-w_(n), and to adapt these weights so as to create a beampattern which is focused on the next largest signal present while havinga null in the direction of the previously largest received signal. Inthe event that the SAT identification indicates that the signal on whichthe beam is currently focused does contain the desired SAT, a trackingsubsystem 75, also a part of focusing subsystem 71, functions withoutre-initialization of the weights to continuously adapt the weights insuch a way as to keep the beam focused on the signal having the desiredSAT irrespective of the fact that the source of this signal may be in astate of motion.

[0033] The adaptive beamforming process proceeds as follows. Theadaptation process constitutes the search for the correct series ofcomplex weights, w_(i), which results in an antenna beam pattern focusedin the direction of the strongest RF signal present in the receiveddata. Ideally, the strongest signal will be the signal the antenna isseeking to detect, that is the one having the expected SAT or identifiertone. In some cases, however, the strongest signal in a cell may beextraneous, that is one originating outside the cell. In such case, theadaptive process will focus the beam pattern in the direction of thisextraneous signal.

[0034] The adaptation process begins by collecting a sequence of vectorsamples, s_(j), and using these vector samples along with an initialweight vector, w_(o), to compute corresponding sequences of the output,y_(j), and the reference signal, d_(j). The data from the vectorsamples, x_(j), and the corresponding reference signal values, d_(j),are then used in a least-squares computation, as hereinafter described,to generate a new weight vector, w_(new). The new weight vector resultsin an antenna beam pattern focused in the direction of the strongest RFsignal present in the received data. While the error, ε_(j), is notnormally computed, it is known from theory that this least-squarescomputation results in a new weight vector that minimizes the sum of thesquared error, S, which is defined as follows: $\begin{matrix}{S = {{\sum\limits_{j}{\varepsilon_{j}\varepsilon_{j}^{*}}} = {{\sum\limits_{j}{\varepsilon_{j}}^{2}} = {{\sum\limits_{j}{{Real}^{2}\left( x_{j} \right)}} + {{Imag}^{2}\left( x_{j} \right)}}}}} & (2)\end{matrix}$

[0035] At the beginning of the adaptation process, the individualweights of the initial weight vector, w_(o), have the following values:w₁=1 and all the other w_(i) are equal to zero. This results in a verybroad initial beam pattern which may admit a number of signals which canbe present within the pattern.

[0036] After the least squares computation leading to new weight vector,w_(new), the beam pattern will have been focused on the largest signalpresent in the received data. A series of data samples is processed withthis new weight vector and the resulting signal processed as hereinafterdescribed to determine which identifier tone is present in the signal onwhich the beam is focused. In the event that this identifier tone is notthe expected tone, it is known that this largest signal is not thedesired signal and the adaptation process is repeated, this timebeginning with the following different initial weight vector.

w_(o)=w_(i)

[0037] where w_(i) is a weight vector orthogonal to the adapted vectorwhich focused the beam on the signal having an incorrect identifiertone.

[0038] The orthogonal weight vector is derived by forming the matrix, P,as follows:

P=I−w _(new) ·w _(new)  (3)

[0039] where I is the identity matrix. When so formed, every column of Pis a vector which is orthogonal to the old weight vector, w_(new), andcan be used as new initial weight vector, w_(i), for the nextadaptation. We have found, however, that some of these vectors in P maylead to a null in the direction of the desired signal as well as to anull in the direction of the largest interfering signal. It has provenmore efficacious to sum the set of column vectors of the matrix, P, anduse this sum as the initial weight vector for the next iteration. Thisset of weights results in a more omnidirectional beam pattern, the maindeparture being the presence of a null in the direction of the largestinterfering signal.

[0040] This differing initial weight vector, after another cycle ofadaptation, in addition to having a null in the direction of the largestsignal present, is focused on the next largest signal present in thereceived data. Additional data is processed with the new weight vectorto determine which identifier tone is present in this next largestsignal. If it too is not the expected identifier tone, the process isrepeated iteratively, each iteration resulting in a beam pattern withnulls in the directions of all signals which have been determined tohave incorrect identifier tones and focused on the next largestremaining signal present in the received data.

[0041] Ultimately this process results in a beam pattern focused in thedirection of the desired signal, that is the signal having the correctidentifier tone. The adaptation process continues at this point, but oneach iteration thereafter, the initial weight vector is the weightvector which resulted from the previous iteration, that is:

w_(o)=w_(previous)

[0042] where w_(previous) is the weight vector resulting from theimmediately preceding iteration.

[0043] As a result, the process continues to focus the beam on thedesired signal and track any movement of the source of the desiredsignal should that source be mobile.

[0044] The concept of orthogonality may be visualized by focusing on arelatively simple situation. The set of weights, wt, can be thought ofas constituting a vector in multi-dimensional space, the number ofdimensions in the space being equal to the number of antenna elements orcorresponding weights, w_(i). In the event that the number of elementsor weights is three, the multi-dimensional space can be readilyvisualized, and has three axes, x, y and z, separated from each other byninety degrees. Let it be assumed that the set of weights which focusedthe beam on the largest interfering signal comprise a vector which liesalong the z axis. Then as the process searches for a new set of weights,w_(i), and a corresponding vector, that vector will be orthogonal to theoriginal vector if it is constrained to lie in the plane defined by thex and y axes.

[0045] Following is the process by which the adaptive antenna proceedsfrom a starting set of weights to a set of weights that focuses the beamon the largest signal present (other than the signal(s) which has beennulled out). Recall that the digitized signal samples from theindividual antenna elements at time j constitute a row vector, x_(j).After collection of a series of sets of such samples, the correspondingrow vectors, x_(j), j=1, 2, . . . , M can be used as the rows of an N=Mmatrix, A. We have observed successful operation of the system where X,the number of such sets, falls in the range eight to 128, but do notbelieve the invention to be so constrained.

[0046] If the individual y_(j) are used as the elements of anM-dimensional column vector, y, this vector is given by the followingrelationship.

y=Aw*  (4)

[0047] Here A is the matrix formed of the input data sample vectors,each corresponding to one of the sees of collected data. The elements ofthe vector, y, are each a sample of the summation of the observed dataafter weighting with the set of weights in use as the data is collected.The vector, w, represents the new set of weights which is to bedetermined.

[0048] The relationship between the vectors ε, y and d is given by:

ε=y=d  (5)

[0049] Substituting (4) in (5) yields:

ε=Aw*−d  (6)

[0050] The squared length of this error vector, ε, is minimized when theerror vector is orthogonal to the column space of the matrix A. Thiscondition is expressed as:

A^(H)ε=0  (7)

[0051] Here the matrix, A^(H), (A Hermitian) is a matrix containingelements, each of which is the complex conjugate of the correspondingelement of the matrix; A, and is further the transpose of the matrix, A,with the conjugated elements. Combining (6) and (7) and solving for w*yields:

w*=(A ^(H) A) ⁻¹ A ^(H) d  (8)

[0052] Here, w* is the optimal least square error weight vector. Thisweight vector results in the best match of the output vector, y, to thevector, d, in the sense that it minimizes the sum of square errors ofEquation (2). From Equation (8), it is seen that w* is a function of thedata matrix, A, and the vector, d. The vector, d, however has beencomputed based upon the previous or initial weight vector, w_(o). Thisprocess could be iterated. That is, starting with an initial weightvector, w_(o), one could take a data set, form A and d, and compute anew weight vector, w₁* by application of Equation (8). Then, using w₁*and the original data set (the same A) compute an improved d, and applyEquation (3) again to compute another new weight vector, w₂*. Thisprocess can be continued until the weight vector does not changesubstantially after each iteration. This has been explored and theconvergence of the process to a stable weight value is quite rapid, Infact, convergence is virtually complete after the first iteration, sorepeated iterations of Equation (8) are not needed or used. Theresulting vector from a single iteration of Equation (8), w*, iscomprised of the set of weights, w₁ which will focus the beam an thelargest signal present (other than signals which have been nulled out ofthe beam pattern by virtue of previous iterations through the adaptiveprocess).

[0053]FIG. 7 is a flow chart summarizing the operation of the adaptivebeam forming process performed in DSP 62. At 100, the process beginswith a set of initial weights. As noted above, this set may have w₁=1and all the other w_(i) equal to zero. At 102, a set of data samplevectors, x_(j) is processed using this initial set of weights. Thisprocessing involves forming the sum of the weighted samples andconverting this sum to a constant modulus version of the sum. Then,using equation (8) at 104, a new set of weights is derived from thesamples of this common modulus version of the sum and from a matrix, A,each of whose rows is one of the vectors, x_(j).

[0054] Next, at 106, additional data samples are processed using the newset of weights, and the SAT frequency present in this processed data isdetermined. At 108, a test is made to determine whether this is the SATassigned to the base station or not. In the event that it is not thecorrect SAT, then it is known that the adaptive beam forming apparatushas formed a beam on an incorrect RF signal. In this event, at 110 a newset of initial weights is formed, this set being constrained to beorthogonal to the set of weights that was used to focus on the incorrectRF signal. This new set of initial weights is chosen to be the sum ofone or more rows of the matrix, P, as defined by equation (3). As aresult of this constraint, the beam pattern formed by the new set ofweights is forced to have a null in the direction of the incorrect RFsignal. The process then returns to step 102 where new input datasamples are processed using the is new set of initial weights.

[0055] This iterative process continues until, at some point, theextraneous RF signals have been nulled in the beam pattern and thepattern focuses on the correct RF signal, that is, the one having thecorrect SAT. At this point a positive result is obtained at test 108,and the process loops back to step 102. Then the process continues toiterate through the loop represented in FIG. 7 so as to continue tomodify the set of weights as necessary such that the beam continues totrack the target RF signal source as it moves about the service region.Note that, when in this made of tracking the desired signal, there is noneed to null out the signal on which the beam has focused since it isfocused on the correct signal. Consequently, there is no need to selecta new set of initial weights at each pass through the loop, since theselection of new weights is only done when one wishes to null out thelargest remaining signal.

[0056] The LSE SAT estimation technique implemented by the system willnext be described. When the beam of the adaptive antenna is focused inthe largest signal present in the received RF energy, the SAT associatedwith that signal will normally be significantly larger than the SATassociated with any other signal which has been suppressed by thefocused beam pattern (typically by 20 dB or more). When the LSE processestimates the amplitudes of any SATs present, one will be found to bematerially larger in amplitude than any of the other two. This then willbe the SAT associated with the signal tracked by the focused beam.

[0057] After the adaptive beam forming process has focused on aparticular signal, the detected output of the adaptive antenna is astream of complex samples (I and Q) designated as the y_(i) in thediscussion above of the adaptive beam forming process, and separated intime by the sampling rate of an A to D converters which digitize theinput signals. The adaptive antenna outputs, y_(j), are then frequencydemodulated to obtain the audio data, which is composed of voice dataand the three sinusoid SAT signals. The complex audio data is then highpass filtered to remove the speech data (below 3,000 Hz) from theremaining SAT composite data (above 3,000 Hz). A model of the receivedsampled composite SAT data is given by:

z=Ax+v  (9)

[0058] where z is the vector of complex composite SAT data samplesreceived from the demodulator and high pass filter output. A is a matrixof complex sinusoids representing the three SATs available in thesystem, x is a vector of complex amplitudes (to be estimated), and v isa vector of complex measurement errors (noise). Following is an expandedversion of this vector-matrix equation. $\begin{matrix}{\begin{bmatrix}z_{1} \\z_{2} \\\vdots \\z_{N}\end{bmatrix} = {{\begin{bmatrix}^{j\quad \omega \quad 1{t1}} & ^{j\quad {\omega 2}\quad {t1}} & ^{j\quad \omega \quad 3{t1}} \\^{j\quad \omega \quad 1{t2}} & ^{j\quad \omega \quad 2{t2}} & ^{j\quad \omega \quad 3{t2}} \\\vdots & \vdots & \vdots \\^{j\quad \omega \quad 1{tN}} & ^{j\quad \omega \quad 2{tN}} & ^{j\quad {\omega 3}\quad {tN}}\end{bmatrix} \cdot \begin{bmatrix}x_{1} \\x_{2} \\x_{3}\end{bmatrix}} + \begin{bmatrix}v_{1} \\v_{2} \\\vdots \\v_{N}\end{bmatrix}}} & (10)\end{matrix}$

[0059] where ω1, ω2, ω3 and x₁, X₂, and X₃, are the radian frequenciesand complex amplitudes of the respective SATs, the ti are the samplingtimes of the i^(th) samples, the z_(i) are the observations (samples),the v_(i) are the complex measurement errors, and N is the number ofsamples taken. Note that this matrix, A, and the vector, x are differentfrom, and not related to, the matrix, A, and the vector, x, which weredescribed above in connection with the beam forming process.

[0060] This is a classic problem of an overdetermined system of linearequations. The problem is said to be overdetermined because there aremany more equations than unknowns. For example, one may take 100samples, resulting in 100 equations, to solve for the three unknowncomplex amplitudes. This type of problem commonly arises from trying tofit a model to measured data.

[0061] If there were no noise or computational roundoff errors in thesystem, the estimation problem could be solved as a system of threeequations in three unknowns:

z_(o)=A_(o)x  (11)

[0062] where A_(o) and z_(o) are A and z formed from three samples(e.g., N=3). This equation could then be solved for the unknownamplitudes contained in x by inverting the matrix A_(o) to obtain

x=A_(o) ⁻¹z_(o)  (12)

[0063] Due to the presence of noise and roundoff errors, a solutionbased on three samples may not be possible because the matrix A_(o) maybecome singular. Even if it is possible, such a solution may not haveacceptable accuracy. The better approach is to take many samples andsolve the resulting equation for the best LSE answer.

[0064] The LSE solution results in an estimate {circumflex over (x)} ofthe parameter vector x such that the (squared) length of the estimationerror vector ε_(z) is minimized, where ε_(z) is given by

ε_(z) =z−A{circumflex over (x)}  (13)

[0065] This is satisfied when the estimation error vector ε_(z) isorthogonal to the column space of the matrix A. This condition isexpressed as

A^(H)ε_(z)=0  (14)

[0066] which results in

A ^(H) z−A ^(H) A{circumflex over (x)}=0  (15)

[0067] This is solved by inverting the matrix ALA, resulting in theestimated value of x given by

{circumflex over (x)}=(A ^(H) A)⁻¹ A ^(H) z  (16)

[0068] This is the desired equation for the least-mean-square-errorestimate of x from the data z and is sometimes called the “normal”equation. It is the projection of the measurement vector z into thecolumn space of the matrix A.

[0069]FIG. 8 is a flow chart illustrating the steps involved inobtaining the estimates of the relative sizes of the SAT tones presentin the received data. At step 120, the adaptive beam forming process asdescribed above is implemented to focus the beam on the largest receivedsignal. Then, at step 122, using the adapted set of weights, w_(i), theprocess acquires a sequence of data samples, y_(j), from the output ofthe adaptive antenna. At step 121, the adaptive antenna output isfrequency demodulated to obtain audio samples. These are high passfiltered to obtain the composite SAT signal comprised of the z_(j)'s.The matrix, A, is then formed at step 124 to have the same number ofrows as there are data samples z_(j) in the column vector, z. Equation(16) is then used at step 126 to develop the LSE estimates of therelative amplitudes of any SAT tones present in the input data. Finally,at step 128, a signal is generated to identify the largest SAT tonepresent and this signal is provided to the beam forming processor.

[0070] The estimation accuracy of this process can also be estimated,giving insight into how many samples must be collected for a givendegree of accuracy.

[0071] From Equation (9), the measurement vector z is composed of Ax(the true value, or the value of measurement one would obtain withouterrors) plus v, a vector or errors. Thus, by substituting Equation (9)into Equation.(16) the estimator is also expressed as

{circumflex over (x)}=(A ^(H) A)⁻¹ A ^(H) z=(A ^(H) A)⁻¹ A^(H)(Ax+v)=x+(A ^(H) A)⁻¹ A ^(H) v  (17)

[0072] This equation states that the estimate {circumflex over (x)} iscomposed of the true value (x) plus (A^(H)A)⁻¹A^(H)v, an estimationerror term. This latter term is the projection of the measurement noiseinto the column space of A. Designating this term as a, the estimator{circumflex over (x)} is thus given by

{circumflex over (x)}=x+u  (18)

[0073] with the estimation error given by

û=(A ^(H) A)⁻¹ A ^(H) v  (19)

[0074] and the error covariance matrix R_(ww) given by

R _(uu) =E{(A ^(H) v[(A ^(H) A)⁻¹ A ^(H) v] ^(x)}=(A ^(H) A)⁻¹ A ^(H) R_(vv) A(A ^(H) A)^(−1H)  (20)

[0075] where E denotes the expected value operation and R_(vv) denotesthe covariance matrix of the measurement noise vector v.

[0076] Assuming that the noise in the vector v is composed ofuncorrelated identically distributed complex gaussian samples, then thecovariance matrix R, of the noise in the estimator is given by σ²I,where I is the identity matrix. The covariance matrix of the estimationerror then reduces to

R _(uu)=σ²(A ^(H) A)^(−1H)  (21)

[0077] The diagonal elements of R_(uu) are the variances of theestimates of the complex amplitudes for the respective estimates (e.g.,the second element on the diagonal is the variance of the 2^(nd)component of {circumflex over (x)}) and the square roots of the diagonalelements are the corresponding (complex) standard deviation values.

[0078] A computer based analysis was performed to explore the behaviorof this estimation procedure. The analysis generates, via computersimulation, a sequence of measurements z formulated via equation (9). Itthen performs two tasks. First it successively generates an estimate{circumflex over (x)} of the complex amplitudes by using Equation (16).FIG. 9 shows the absolute values of the estimates as a function of thenumber of samples used to formulate the estimates (expressed as time,0.0001 second per sample). As expected, the longer the time series usedto form an estimate, the more accurate the estimate becomes. When thenumber of samples reaches 50 (a sampling time of 0.005 seconds) thediffering levels of signals are substantially resolved.

[0079] Secondly, the computer based analysis plots the estimate standarddeviations obtained from diagonal elements of the matrix R_(ww) as givenin Equation (14). FIG. 10 shows the standard deviations, also as afunction of the number of samples used to form the estimate. Thesevalues are in dB relative to the estimates. Table 1, below, shows theparameters used for this analysis. TABLE 1 Parameters of the ComputerAnalysis Frequency Power Phase (Hz) (dBnoise) (Degrees) Signal 1 597024  137 Signal 2 6000 3  37 Signal 3 6030 1 150 Measurement Noise σ² = 1— (0 dB) Sample Frequency 10000  — —

What is claimed is:
 1. A communication system for receiving an inputwhich includes a desired signal as well as interfering signals, at leastsome of said desired signal and interfering signals having associatedtherewith one of a plurality of identifier components, the identifiercomponent associated with said desired signal being different than theidentifier components associated with at least some of said interferingsignals, said system comprising: a. an identifier subsystem which uses asuperresolution process for estimating the relative magnitudes of theidentifier components associated with the desired signal and interferingsignals which may be present; b. a receiver subsystem for receiving saidinput and for converting the input to a form usable by said identifiersubsystem; and c. apparatus responsive to the relative magnitudeestimates produced by said identifier subsystem and operable tofacilitate the communication function of said system.
 2. Thecommunication system of claim 1 wherein said superresolution process isa least square error estimation process.
 3. The communication system ofclaim 1 wherein said desired signal and at least some of saidinterfering signals each comprises a frequency modulated RF signal andwherein said receiver subsystem downconverts said frequency modulated RFsignals to baseband signals which are then digitized and supplied tosaid identifier subsystem.
 4. The communication system of claim 1wherein said receiver subsystem includes a receiving antenna and afocusing subsystem to aim the beam pattern of said antenna in thedirection of the source of said desired signal, said focusing subsystembeing responsive to the magnitude estimates provided by said identifiersubsystem to determine when said beam pattern is so aimed.
 5. Acommunication system for receiving an input which includes a desiredsignal as well as interfering signals, at least some of said desiredsignal and interfering signals comprising signals which are frequencymodulated by one of a plurality of identifier components, the identifiercomponent modulating said desired signal being different than theidentifier components modulating at least some of said interferingsignals, said system comprising: a. a receiver subsystem fordownconverting said frequency modulated signals to lower frequencysignals and for digitizing said lower frequency signals; b. a processorwhich is responsive to said digitized signals to estimate the relativemagnitudes of the identifier component used to frequency modulate saiddesired signal and of the identifier components used to frequencymodulate said interfering signals, said processor utilizing asuperresolution process; and c. apparatus responsive to the relativemagnitude estimates made by said processor to facilitate thecommunication function of said system.
 6. The communication system ofclaim 5 wherein said superresolution process is a Least square errorprocess.
 7. The communication system of claim 5 wherein said processoris a digital signal processor.
 8. The communication system of claim 5further comprising a receiving antenna and a subsystem to aim the beampattern of said antenna in the direction of the source of said desiredsignal, and wherein said focusing subsystem is responsive to themagnitude estimates provided by said identifier subsystem to determinewhen said beam pattern is so aimed.
 9. A communication system forreceiving input data which includes a desired signal as well asinterfering signals, at least some of said desired signal andinterfering signals having associated therewith one of a plurality ofidentifier tones, an identifier tone associated with said desired signalbeing different than the identifier tones associated with at least someof said interfering signals, said system comprising: a. an identifiersubsystem including a processor and operative to estimate the relativemagnitudes of the identifier tones associated with the desired signaland interfering tones which may be present, said processor beingoperative to: i) form a matrix, A, of complex sinusoids representing thevarious tones which may be included in said input data, ii) form acolumn vector, z, the elements of which comprise digital samples of saidinput data, iii) define a column vector, {circumflex over (x)}, theelements of which are the magnitudes of the tones to be estimated, andiv) determine the relative magnitudes of the various tones using therelationship: {circumflex over (x)}=(A ^(H) A)⁻¹ A ^(H) z where: A^(H)is A Hermitian; b. a receiver subsystem for receiving said input dataand for converting the input to a form usable by said processor; and c.apparatus responsive to the relative magnitude estimates produced bysaid identifier subsystem and operable to facilitate the communicationfunction of said system.
 10. The communication system of claim 11wherein said processor is a digital signal processor.
 11. A method ofoperating a communication system which receives an input including adesired signal as well as interfering signals, at least some of saiddesired signal and interfering signals having associated therewith oneof a plurality of identifier components, the identifier componentassociated with said desired signal being different than the identifiercomponents associated with at least some of said interfering signals,said method comprising the steps of: a. receiving said input andconverting it to a form usable for further processing; b. operating ansaid converted input with a superresolution process to estimate therelative magnitudes of the identifier components associated with thedesired signal and any interfering signals which may be present; and c.utilizing the relative magnitude estimates to facilitate thecommunication function of said system.
 12. The method of claim 11wherein said superresolution process is a least square error process.13. The method of claim 11 wherein said desired signal and at least someof said interfering signals each comprises a frequency modulated RFsignal and wherein said step of converting comprises downconverting saidfrequency modulated RF signals to lower frequency signals and digitizingthe downconverted signals for use in said superresolution process. 14.The method of claim 11 wherein said input is received with an antennaand wherein said step of utilizing the relative magnitude estimatescomprises at least the step of utilizing the relative magnitudeestimates to aim the beam pattern of said antenna in the direction ofthe source of said desired signal, said estimates being used todetermine when said beam pattern is so aimed.